The projected explicit Itô-Taylor methods for stochastic differential equations under locally Lipschitz conditions and polynomial growth conditions

DOI10.1016/J.CAM.2018.08.057zbMath1404.60083OpenAlexW2890537485MaRDI QIDQ1757364

Minggang Han, Qiang Ma, Xiao-Hua Ding

Publication date: 4 January 2019

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2018.08.057

zbMATH Keywords

stochastic differential equationsprojected explicit Itô-Taylor methodsstochastic B-consistencystochastic C-stability

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (4)

On numerical methods to second-order singular initial value problems with additive white noise ⋮ On the approximations of solutions to stochastic differential equations under polynomial condition ⋮ Split-step balanced \(\theta \)-method for SDEs with non-globally Lipschitz continuous coefficients ⋮ A stochastic Gronwall inequality and applications to moments, strong completeness, strong local Lipschitz continuity, and perturbations

Cites Work

• Order-preserving strong schemes for SDEs with locally Lipschitz coefficients
• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
• Theta schemes for SDDEs with non-globally Lipschitz continuous coefficients
• The truncated Euler-Maruyama method for stochastic differential equations
• Convergence and stability of the semi-tamed Euler scheme for stochastic differential equations with non-Lipschitz continuous coefficients
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Almost sure exponential stability of neutral stochastic differential difference equations
• Stochastic C-stability and B-consistency of explicit and implicit Milstein-type schemes
• B-convergence of split-step one-leg theta methods for stochastic differential equations
• Stochastic C-stability and B-consistency of explicit and implicit Euler-type schemes
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• The tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients
• A Fundamental Mean-Square Convergence Theorem for SDEs with Locally Lipschitz Coefficients and Its Applications

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